Rapper Mr Michel, 50, is accused of taking money from a Malaysian tycoon, Jho Low, to carry out a political influence campaign in the US.
He denies charges including conspiracy and witness tampering.
Mr DiCaprio, 48, is not accused of wrongdoing and is appearing as a witness.
Mr Low - who is currently a fugitive and believed to be in china - is a co-defendant in the case. Authorities believe the financier used his vast resources to curry favour among celebrities including Mr DiCaprio and model Miranda Kerr.
In court on Monday, a soft-spoken, bearded Mr DiCaprio - who described himself simply as "an actor" - told jurors that he first met Mr Low at a party in Las Vegas in 2010.
In subsequent years, he attended "a multitude of lavish parties" on yachts and nightclubs at Mr Low's invitation alongside other celebrities, actors and musicians.
On one occasion, Mr DiCaprio attended a New Year's Eve party in Australia with Mr Low, after which partygoers were flown to the US in an effort to celebrate New Year's twice.
The actor's 2013 film Wolf of Wall Street was partially funded by a firm tied to Mr Low.